Suppose that the f(x) = A x B^x if f(x) passes throught the points (4,7) and (7,12) find a = (round to the 4 decimal place)

Question

Suppose that the f(x) = A x B^x if f(x) passes throught the points (4,7) and (7,12) find a = (round to the 4 decimal place)

Answer 1

y = ab^x for the point (x,y)

7=ab^4 for the point (4,7)

12 =ab^7 for the point (7,12)

a = 7/b^4 = 12/b^7

b^7/b^4 = 12/7

b^3 = 12/7

b = cube root of 12/7 = 1.1968

a = 7/b^4 = 7/(1.1968)^4 = 3.4118

f(x) = 3.4118(1.1968)^x